Completed Projects

Principal investigators: Chandra Orrill (Rethink Learning Inc.), Shakhnoza Kayumova, Pratim Sengupta (University of Calgary)

Funding agency: National Science Foundation - EAGER program

Abstract: As reliance on technology increases across society, it is critical to develop a population that is more knowledgeable about and engaged in the topics of cybersecurity and artificial intelligence (AI). The aim of the Opening Doors project is to engage industry professionals in the fields of cybersecurity and AI in conversations with educational researchers, AI and cybersecurity researchers, and K-12 teachers. These conversations will serve as a means to identify disciplinary knowledge, including needs and benefits, at the intersection of cybersecurity and AI. The group will work to identify ways to engage middle school students and their teachers in learning about AI, cybersecurity, and the intersections between them. By including this array of voices, the project will generate knowledge about the differences and similarities between industry and academic expectations. The discussion will also drive the development of a survey that can be used to determine what students know about AI and cybersecurity as well as a proof-of-concept instructional module that addresses one of the identified gaps in knowledge. The project team will also document the process for building this interdisciplinary community of practice to focus on a single issue in ways that shape students’ educational experiences. The project will determine whether investing effort into deciphering what middle school students do know, and what they can know, will lead to students who are more engaged in cybersecurity and AI as citizens, users, programmers, or in other roles as they mature into adulthood. The outcomes of this project will advance understanding of the nature of expertise of researchers and professionals in AI and cybersecurity, as well as supporting and studying communication between them, while exploring ways to translate that expertise into curricula for widespread dissemination to middle school teachers and students. The project team will use a combination of qualitative and quantitative approaches to accomplish the following outcomes: (1) the development of an interdisciplinary think tank along with a documented process for creating it that can inform others interested in building similar partnerships; (2) the development of survey instruments designed to uncover what middle grades students understand about AI, cybersecurity, and the intersection of these two areas as they affect their lives, as well as possible careers available in this interdisciplinary space; (3) findings from the survey on possible gaps as well as what middle grades students understand about these areas; and (4) one proof-of-concept learning module that can be implemented by any middle school teacher anywhere.

Principal investigators: Mia Dubosarsky (Worcester Polytechnic Institute), Gillian Smith (Worcester Polytechnic Institute), Shakhnoza Kayumova (UMass Dartmouth)

Funding agency: National Science Foundation

Abstract: This project aims to broaden pre-K-5 students' participation in standards-aligned and culturally responsive computational thinking (CT). The research team will establish a research-practice partnership (RPP) that will co-plan and co-design multidistrict efforts to develop standards-aligned and culturally responsive professional development (PD) that integrates CT into the PK-5 curriculum and instruction. The populations served are pre-K-5 students and teachers in Central Massachusetts. The project will connect a diverse team of researchers, policymakers, professional development coaches, and educators with diverse expertise on pre-K-5 CT teaching and learning. Following guidelines for effective partnerships and guided by Design-Based Implementation Research (DBIR) and Participatory Research, the project has four phases: 1) Build relationships within the RPP. 2) Identify problems of practice, and conduct in-school research. 3) Co-create PD in an iterative process of creating-testing-revising solutions to the identified problems. 4) Disseminate results and sustain the RPP. The central research question asks what factors enable and hinder successful collaborations between institutions of higher education, school districts, and the Massachusetts Department of Elementary and Secondary Education to address problems of practice around culturally and linguistically responsive CT teaching and learning in pre-K-5 classrooms. The RPP will develop shared understanding about the specific challenges that pre-K and elementary teachers and administrators from rural, urban, and town districts face concerning teaching CT to diverse populations. Such a knowledge base is essential to the development of CT-focused PD to empower teachers to integrate CT into curricula in accessible and meaningful ways. Using the RPP frameworks of mutualism and DBIR approaches of systematic and repeated inquiry, project members will identify and research problems of practice and possible solutions and strategies in their context. Analyses of the principles and processes will add to the body of knowledge about implementation research on building capacity of RPPs to identify and address problems of practice on culturally and linguistically responsive PD on CT integration for pre-K-5. This project is funded by the CS for All: Research and RPPs program.

Principal investigators: Chandra Orrill (Rethink Learning Inc.) with Yasemin Copur-Gencturk (University of Southern California, Project PI), Benjamin Nye (University of Southern California), and Allan Cohen (University of Georgia)

Funding agency: Institute of Education Sciences

Abstract: The purpose of this program is to increase middle school teachers’ content and pedagogical content knowledge of proportional reasoning and, in turn, improve their students’ understanding of proportional reasoning by developing an interactive, personalized computer-based professional development (PD) program for teachers. This intervention will surpass past
attempts to provide PD to improve student learning by building on an in-depth review of professional learning opportunities known to be effective in improving teacher knowledge and student learning and by creating an interactive, personalized, computer-based professional development program that can be accessed by any teacher. The goal of this four-year project is to develop and test an interactive, personalized computer-based professional development program for middle school teachers. The system will be usable for teachers, feasible for use in various settings including the home, and easily accessible for all end users. The purpose of the program is to increase middle school teachers’ content and pedagogical content knowledge of proportional reasoning and, in turn, improve their students’ understanding of proportional reasoning. This proposal responds to the needs facing middle school students and their teachers in multiple ways and has the potential to contribute to an improvement in student mathematics outcomes by enhancing teachers’ knowledge associated with the core tasks of mathematics teaching and student mathematics achievement. Importantly, the project will contribute important findings to professional development research regarding the effectiveness of a computer-based program that provides interactive, virtual facilitation.

Principal investigators: Shakhnoza Kayumova (PI) with Ramprasad Balasubramanian (ENG), Raymond Laoulache (ENG), Walter Stroup (STEM Ed & Teacher Development), Qinguo Fan (BNG), Maoyuan Sun (CIS)

Funding agency: Multidisciplinary Seed Funding. University of Massachusetts Dartmouth

Abstract: The goal of this multidisciplinary project is to design and implement socially and culturally response-able, learning-by-making and design-based approach to robotics, engineering, and science practices in the context of life sciences, which aims at supporting girls’ equitable participation and identity development in STEAM disciplines.

Principal investigators: Walter Stroup (UMass Dartmouth), Uri Wilensky (Northwestern University), Tony Petrosino (UT-Austin), Corey Brady (Vanderbilt University)

Funding source: National Science Foundation

Abstract: Group-Based Cloud Computing (GbCC) is agent-based modeling program, powered by NetLogo Web, that allows learners to work collaboratively to participate in, author, and share models. Models developed in NetLogo Web cover a range of domain content including, but not limited to: disease transmission, population dynamics, physical phenomena, and social stratification. GbCC provides network supported, generative design based learning and teaching opportunities. This project seeks to use GbCC technologies to encourage teachers and students to participate more fully in socially mediated learning and teaching to broaden and deepen interest in authentic STEM fields, learning, and careers. The goal of the project is to use the browser-based GbCC capabilities to advance participatory and more fully socially mediated approaches to learning and teaching in STEM classrooms as a vehicle to broaden and deepen the involvement and engagement of all students with in-depth understanding of STEM domains and their possible STEM-related careers.

Principal investigators: Chandra Orrill (Rethink Learning Inc.) with Yasemin Copur-Gencturk (Project PI – Univ of Southern California); Allan Cohen (Univ of Georgia); and Jonathan Templin (Univ of Iowa)

Funding agency: National Science Foundation

Abstract: The overall goal of this project is to pursue a potentially transformative approach to assessing teachers’ knowledge by developing a measure that is closely aligned with the content and skills taught in PD programs. This instrument will employ emerging psychometric models. Specifically, we aim to blend features of diagnostic classification models (DCMs) and statistical topic models (STMs) to provide informative feedback about teachers’ learning and to identify patterns in their knowledge growth. Using DCMs involves specifying the fundamental components of reasoning in a particular domain, and then constructing test questions systematically to correspond to reasoning with a different combination of those components. In contrast, STMs involve analyzing the patterns in responses to provide insights into the reasoning teachers use in giving their answers. By developing open-ended items, we will create items that capture the key components of teachers’ content and pedagogical content knowledge in proportional reasoning, and then identify the characteristics of reasoning among teachers with different levels of content and pedagogical content knowledge.

Principal investigators: Chandra Orrill (Rethink Learning Inc.)

Funding agency: National Science Foundation

Abstract: The Proportions Playground project seeks to both develop a unique pilot software application for the iPad and explore how it supports teachers in developing a coherent, robust definition of proportions. The software will be designed to support either numeric manipulation (e.g., graphing software) or geometric constructions (e.g., dynamic geometry software). Specifically, for this project the mathematics of interest will include the relationships between similarity and proportion and the nature of covariation. The research will focus on how teachers are developing a robust and coherent understanding of proportions and how the dynamic environment promotes such understandings. Working with six teacher advisors, the project will develop three task sets. Using teaching experiments and individual interviews, results will be used to refine the task sets. The revised task sets will be piloted with 40 teachers. Data will be collected on participants' thinking and any changes seen in the knowledge resources they are using. The researchers will be looking for factors that seem to impact teachers' thinking as well as evidence to support or deny the assertion that the Proportions Playground activities engage teachers in (a) different ways of reasoning about proportions and (b) support them in drawing from a wide array of resources so that coherence may be developed were the teachers to have a prolonged engagement with the tools. The project will rely on Epistemic Network Analysis to identify the connections between knowledge resources.

Resources

•  Proportions Playground apps

Principal investigators: Stephen Witzig (PI) with Tesfay Meressi (Co-PI); Kym Welty (Program Coordinator); Sharon Hartley (Teacher Leadership Specialist); David Welty (STEM Education Consultant); Annette Brickley (STEM Education Consultant)

Funding agency: National Science Foundation

Abstract: The University of Massachusetts Dartmouth has been engaged in a multiyear partnership to train a cohort of Teaching Fellows (TFs) and Master Teaching Fellows (MTFs) as STEM Educators for the middle and secondary schools of Fall River, New Bedford, and Wareham Massachusetts. In these three districts, 50-77% of students are economically challenged (high-needs). While success in the STEM subjects could provide a route toward college and careers for many of these students, they consistently score far below state averages when tested in STEM subjects. There is a critical need in these districts to prepare STEM educators to engage the student population in STEM disciplines.

The three goals of this professional development project are to: (1) Deepen STEM Content Knowledge and instructional practices through myriad content-intensive learning experiences; (2) Develop Critical 21st Century Skills through the active exploration of emerging technologies in STEM education; and (3) Develop Teacher Leadership Skills via a collaborative approach, based on a proven model that utilizes peer-coaching, mentoring, and professional learning communities.

Principal investigators: Jim Kaput, UMass Dartmouth, Jeremy Roschelle, SRI International (Co-PI)

Funding: National Science Foundation

Abstract: Prior SimCalc work exploited the representational affordances of the computational medium to democratize access to the core ideas leading to and underlying Calculus. These important ideas had previously been sequestered in a capstone course reached by at most 10-12% of the population, but now can be successfully mastered by urban middle school students if given the opportunity. Simulations, new graphical ways of creating and editing functions (as well as derivatives and integrals of functions), and dynamic visualization tools together enabled a reconstituting of these ideas into core curriculum beginning in the middle grades. We have now begun to study the profound potential of combining the previously established representational innovations with the new connectivity affordances of increasingly powerful, robust and inexpensive hand-held devices in wireless networks. In combination with the representational affordances, we see classroom connectivity as a critical ingredient to unleash the long-unrealized potential of computational media in education, because its potential impacts are direct and at the communicative heart of everyday classroom instruction. This will happen only if those impacts are sufficiently understood to inform iterative improvement of technologies and classroom practices, as well as design of teacher development and support structures that support and do not impede learning.

Principal investigators: Stephen Hegedus, (UMass Dartmouth), James Kaput, (UMass Dartmouth)

Funding: National Science Foundation

Abstract: This project builds on CC1 by continuing to develop dynamic mathematical environments integrating the latest advances in wirelessly connecting hand-held devices and desktop PCs. We are investigating the impact of new activity structures arising from such development, on students’ participation, engagement and learning, in various algebra and precalculus classrooms in schools and university.

Principal investigators: Andrew Izsak - PI (University of Georgia), Joanne Lobato, (San Diego State University), Chandra Orrill, (UMass Dartmouth), Allan Cohen (University of Georgia), Jonathan Templin (University of Georgia)

Funding: National Science Foundation DR-K12 Program

Abstract: Diagnosing Teachers’ Multiplicative Reasoning (DTMR) is an exploratory project that addresses the assessment component of the DR-K12 Contextual Challenges strand. Investigating knowledge that teachers need to enable students’ learning and developing assessments of that knowledge are central challenges for mathematics education. One approach, driven by accountability, emphasizes correlations between amounts of teachers’ knowledge and students’ achievement. Another, grounded in research on mathematical thinking, often uses case studies to investigate teachers’ capacities for identifying and building upon opportunities in students’ problem-solving strategies. Tensions exist between these approaches because instruments convenient for assessing large numbers of teachers are insensitive to capacities for reasoning, while case study methods used to investigate teachers’ reasoning are not practical with large samples. The DTMR project will build a demonstration instrument both suitable for use with large samples of teachers and informative about their capacities to reason about content in ways that support students’ thinking.

Principal investigators: Chandra Orrill,(UMass Dartmouth), Andrew Izsak, (University of Georgia), Allan Cohen, (University of Georgia)

Funding: National Science Foundation Research and Evaluation on Education in Science and Engineering Program

Abstract: The connection between teacher professional development and student achievement is not well understood. Gaining insight into this connection is crucial if we are to help in-service teachers develop further understandings of content that they can use to support their students’ learning. We propose to develop and refine methods for empirically examining relationships among teacher professional development, teacher learning, teacher practice, and student achievement. We will do so by examining three questions as we offer the NSF-funded InterMath professional development program to middle-grades teachers in Atlanta Public Schools:

1. What do the teachers learn from InterMath experiences?
2. If the teachers learn from InterMath, do their instructional practices change as a result?
3. If the teachers’ practices change, are there measurable changes in students’ achievement?

The proposed project will concentrate on the InterMath-Rational Numbers course, a 50-hour course aimed at developing teacher content knowledge about numbers including fractions, decimals, percents, ratios, and proportions. The course provides teachers experiences as learners in classes where the instructor models reform-oriented practices such as asking for multiple solution strategies for open-middle problems. The course also makes regular use of technologies such as spreadsheets and Graphing Calculator software. We will study four implementations of the InterMath-Rational Numbers course that we offer to 6th- and 7th-grade teachers, and we will compare these teachers to those in control groups. Primary data for answering Question 1 will come from repeated measures using the NSF-funded Content Knowledge for Teaching Mathematics assessment developed at the University of Michigan, as well as observations of and interviews with teachers while taking the InterMath course. Primary data for answering Question 2 will come from surveys and classroom observations before and after the InterMath course. Primary data for answering Question 3 will come from state-wide achievement tests and an instrument we develop to measure students’ conceptual understanding and problem-solving skills. A unique aspect of our design is the use of latent group analyses to detect subgroups of teachers who evidence similar response patterns across items on the Content Knowledge for Teaching Mathematics assessment. We will use these subgroups to construct matched treatment and control groups. Thus we will collect an extensive body of data with which to gain insight into the links between professional development, teacher learning, teacher practice, and student achievement.

Principal investigators: Stephen Hegedus, (UMass Dartmouth), Nicholas Jackiw, (KCP Technologies)

Funding Source: National Science Foundation Research and Evaluation on Education in Science and Engineering Program

Abstract: Building on prior work, we plan to develop a rich technological environment that combines the dynamic geometry environment of Geometer’s Sketchpad® with haptic technology, particularly force feedback devices. We plan to create a series of geometric activities specifically focused on 2D figures and shapes as well as some simple 3D surfaces and solids, to enable users of various ages to explore the properties of these objects with various senses. The project combines these technology goals with learning goals that aim to provide better access to a wider variety of students (including underrepresented groups) in science, engineering and mathematics. We will conduct a series of informal after-school experiments at the Kaput Center for Research and Innovation in STEM Education, and then some formal classroom interventions with primary school students in various schools. We will also explore extensions of these activities in some engineering and mathematics undergraduate classrooms at the University of Massachusetts. We will document, using data collected from the technological environment and other instruments, how students discover properties of mathematical objects within this new environment and develop formal argumentation, how this varies across age group, and how it can be integrated into formal classroom settings. The data will also be used to refine the design of the system over 3 years. We aim to discover what impact fusing a second modal input of feel to sight affords in terms of engaging students of a variety of ages into exploring geometric concepts, and observe what kinds of mathematical activity can be designed that are significantly different to those using traditional forms of instruction. We will evaluate the practicality and educational benefits from integrating such technology. We integrate and build upon over 15+ years of research and development of the SimCalc Projects at the Kaput Center and the Geometer’s Sketchpad® software, particularly Sketchpad’s huge impact and adoption by classrooms across the world.

Principal investigators: Jeremy Roschelle (SRI International), Chris DiGano (SRI International), Roy Pea (SRI International), Jim Kaput (UMass Dartmouth)

Funding: National Science Foundation

Abstract: The Educational Software Components of Tomorrow (ESCOT) project investigated fundamental social, economic and technical issues which affect the ability of the National Science Foundation (and its extended community) to meet the need for software that supports systemic reform. The report of the President’s Committee of Advisors on Science and Technology (PCAST, 1997) highlights the failure of the marketplace to deliver enough “student-centered, constructivist” software, particularly with respect to the innovative curricula and national standards that are now entering implementation. PCAST calls for federal funding of “exploratory work focusing on the development and preliminary testing of innovative new approaches to the application of technology in education which are unlikely to originate from within the private sector.” The REPP announcement likewise calls for research aimed at “discovering and examining the prerequisites for implementing sustainable reform on a national scale; untapped, appropriate, and efficient uses of technology.” ESCOT created a testbed for exploring an emerging convergence of powerful, but untapped forces: dynamic media, knowledge networks, and component software architectures. Together these forces have the potential to reshape the infrastructure for sustainable development of educational software, resulting in a new network economy. This network economy could meet national needs for educational software with greater efficiency, capacity for innovation, and competitive drive towards quality. In addition to forming the experimental testbed, ESCOT pursued three objectives: (a) developing a map for expressing the needs of standards-based reform efforts in relationship to conceivable software modules; (b) understanding how to use the internet to catalyze distributed, self-organizing authoring teams; and (c) analyzing mechanisms and design patterns for achieving interoperability among educational software components. Paralleling and extending the initial NSF curriculum development support strategy, the ESCOT testbed operated within a focussed scope, existing middle school mathematics curriculum and implementation projects, with the goal being to provide knowledge and exemplars that inform policy and practice more broadly in K-12 mathematics and science.

Director: Chris Mars, Wareham High School
Co-Director/Higher Ed Partner: Stephen Hegedus, Mathematics Department, University of Massachusetts Dartmouth

Funding: Massachusetts Department of Education, Title IIB Mathematics and Science Partnership grant

Principal investigators: Ricardo Nemirovsky, TERC, Jim Kaput, UMass Dartmouth (Co-PI)

Funding: National Science Foundation

Abstract: The aim of this project is to investigate new approaches to nurture and cultivate the mathematical imagination of all students. Mathematics as a science to imagine-with is not incompatible with memorizing the multiplication tables, number facts, or shortcuts to operate fractions, but it changes what these memories are part of. It is about imagining space and time: shapes, patterns, or trajectories; it is about envisioning how things could be; it is about discriminating the finite and infinite, the discrete from the continuous, and the possible from the impossible. The main conjecture of this is that cultivating mathematical imagination is deeply related to enriching bodily action/perception. The proposed research intends to investigate this thesis through a series of studies with high school students and pre-service teachers. It is widely acknowledged that an essential goal of pre-service teacher education involves reconstituting prospective teachers’ mathematical knowledge to serve as a foundation for teaching. Indeed, mainstream pre-service teacher education makes creative use of manipulatives to achieve this revisiting of important ideas in ways that also inform pedagogy—how to teach those ideas. Thus, for example, the geoboard is commonly used to revisit rational number ideas, to help deepen understandings of area and perimeter, and, as importantly, to build teachers’ understanding of the roles of manipulatives—how to relate the physically-based actions to mathematical notations, how to use them to diagnose confusions (e.g., between area and perimeter, or between a fraction-as-operator and fraction-as-quantity), how to integrate their use productively and pragmatically in real classroom situations, etc.

Principal investigators: Maria Blanton, UMass Dartmouth, Despina Stylianou CCNY-CUNY (Co-PI)

Funding: National Science Foundation ROLE Grant

Abstract: The Proof Project investigates the development of students’ understanding of proof during the undergraduate experience. Proof, arguably, lies at the heart of mathematics; it pervades all mathematical work and sets mathematics apart from all other sciences. As such, it is necessary for all students to develop both the understanding of concepts related to proof and the skills to read and write proofs. The Proof Project aims to examine the ways in which undergraduate students acquire and develop their understandings of the concept of proof and to provide suggestions for the types of curricular and pedagogical innovations that can make the mathematics of proof accessible to all students.

Research and development in technology and curriculum dedicated to democratizing access to the Mathematics of Change and Variation, including ideas underlying Calculus.

Principal investigators: Stephen Hegedus, UMass Dartmouth, Gary Davis, UMass Dartmouth

Funding: National Science Foundation

Abstract: The project funded two symposia over the course of one year and brought together a select group of seminal thinkers in symbolic cognition in undergraduate mathematics, for the purpose of establishing a research agenda in this new line of inquiry. Symbolic cognition in mathematics is concerned with the evolution and use of mathematical symbols, especially their practical side – the specific cognitive and communicative roles that symbols play in helping people to do mathematics and learners to learn undergraduate mathematics. Building on 3 years of work (2001-2003) at the annual meetings of the International Group for the Psychology of Mathematics Education (PME), we assembled an international group of scholars from the fields of mathematics and mathematics education, for the purpose of critically examining the major research themes emerging from the PME working group meetings, and to develop and produce a seminal work on the use of symbols in undergraduate mathematics instruction that will have theoretical and practical implications. Our intention was that this international working group would be able, through its focus on research and writing, to bring the issues of symbolic cognition in undergraduate mathematical thinking to a point where it is highly visible and on the agenda of all teachers of undergraduate mathematics through collaboration with national organizations such as the American Mathematical Society.

Principal investigator: Stephen Hegedus, UMass Dartmouth

Funding: University of Massachusetts President’s Office Professional Development Grant

Abstract: Our project utilizes the latest wireless technology from Texas instruments, TI Navigator, a system that connects students’ work on hand-held devices (primarily the TI-83/84 graphing calculator) to a host computer so that whole-class contributions can be displayed. Students can instantly see how their work compares with contributions of their peers, a feature that enhances cooperative teamwork and acquisition of skills, so critical to student learning in mathematics, engineering and science. The system supports a very flexible use of different contributions to class presentations and discussions by both students and teachers. The mathematical representations that can be utilized in the system allow activities in a broad cross-section of curriculum, including algebra, geometry, pre-calculus and Calculus, to be introduced in different, and more powerful ways. Teachers can see quickly what their whole class is thinking, diagnose common errors and support active participation and discussion. We will build new curriculum that utilizes this technology and integrate it into core mathematics courses across campus, investigating the impact on student learning and engagement as well as faculty professional development. Initially we will begin with Impulse Calculus I, where teamwork and student interaction is already a central part of the undergraduate program. This project builds on prior successful work in local High schools and a strong relationship with Texas Instruments. We will work in classrooms of various faculty then host a 1-day workshop on Campus in partnership with the Center for Teaching Excellence to instruct more faculty how to use such technology. We will work with other Campuses throughout the year, demonstrating the use of such technology in relevant classrooms.

Principal investigators: Chandra Orrill, UMass Dartmouth

Funding: National Science Foundation CAREER

Abstract: This research project aims to explore a hypothesis about mathematics teacher knowledge formed through work with teachers both in research settings and in professional development. The hypothesis is that being a good mathematics teacher requires not only developing a certain body of knowledge, but also having mapped that content into a coherent and connected understanding of the domain that includes insights into what the content being taught grows out of and where it goes next. Specifically, in this project, we will focus on middle grades teachers’ knowledge of proportional reasoning. A mixed methods approach will be used in the first phase to develop profiles of understanding that highlight not only the body of knowledge teachers have developed, but also the connections among facets of that knowledge. Once those profiles are complete, phase 2 will focus on looking at teachers’ practice to develop interconnected profiles of understanding that consider not only the ways in which teachers understand the domain, but also how those interconnected understandings manifest themselves in the classroom. The hypothesis is that teachers with more connections in their understanding will have more tools to draw upon in their classroom teaching, thus using their knowledge in different ways from teachers with a less coherent understanding.

Resources

Below you will find some of the resources that have been developed as a result of this project.

• Face-to-Face Interview Protocol (PDF)
• Livescribe Interview Protocol (PDF)
• Fraction Bars